Method for changing the polarization of at least one of the photons emitted from a photon-pair source into various partial paths of rays, and method for optionally generating individual photons or photon pairs in an optical channel

ABSTRACT

A method is provided for changing the polarization of at least one of the photons emitted from a photon pair source into various partial ray paths using an electro-optical modulator (EOM), which is positioned in the particular partial ray path being traversed by the photon to be influenced and which, in the activated state, is able to alter the polarization of a photon, the modulator being activated as a function of time such that the probability that the photon is found in the region of the electro-optical modulator in the activated state is at a maximum.

FIELD OF THE INVENTION

The present invention relates to a method for changing the polarizationof at least one of the photons emitted from a photon-pair source intovarious partial paths of rays. The present invention also relates to amethod for optionally generating individual photons or photon pairs inan optical channel.

BACKGROUND INFORMATION

The so-called quantum computer is of considerable interest for thedevelopment of calculating machines. In quantum computers, logicoperations are performed on the basis of quantum states and byselectively Influencing such states. Quantum states may be described asresulting from the superposition of a large number of normalized,orthogonal base states, whose weighting is accomplished by probabilitymasses which are definable by measuring processes. In quantum computers,the fundamental unit that corresponds to the binary bit, i.e., thefundamental unit for all arithmetic operations in traditional electroniccomputers, is the “quantum bit” (qubit). The quantum bit can berepresented, in this context, as a linear, weighted, superposed state oftwo basic functions, namely of the basic functions “0” and “1”. Thebasic functions correspond to the classic values 0 and/or 1 of the bit.The complex coefficients correspond to the weights with which the basicfunctions participate in the superposed state. The reference V. Vedralet al., Basics of Quantum Computation, Progr. In Quantum Electronics 22,1 (1998), purportedly describes the fundamentals of the quantumcomputer.

An example of such a quantum state, which can be described as asuperposition of two orthogonal basic functions, is the polarizationstate of light. Quantum bits can, therefore, be implemented as thepolarization states of individual photons and as logic operationsresulting from manipulation of the photons or photon pairs. Asmathematical-topological equivalents, quantum bits are represented onthe Bloch sphere and polarization states on the Poincare sphere assurface points.

By using light as the basis for a quantum computer, one derives thebenefit of being able to selectively influence the polarization state ofa single photon, emitted from a photon-pair source.

Another property of light, in this connection, may be that polarizationstates are correlated within one photon pair stemming from a singledecay. The photon pair is quantum mechanically in a so-called“transposed state”, which can be used as the starting state for thequantum computer.

A photon pair source is produced, for example, by an opticallynon-linear crystal in conjunction with an intensive optical pump lightsource, usually a laser light source. Under suitable geometricconditions, a single photon of the pump light source decays with acertain probability, while retaining energy and pulse, into two energyquanta or photons. The reference H. Paul, Nonlinear Optics, vol. 2, page94 ff, Berlin 1973, purportedly describes this phenomenon as parametricfluorescence. The fluorescent light is emitted with two main frequenciesor wavelengths, which differ depending on the excitation geometry, indefined spatial directions, relatively to the direction of propagationof the pumping beam. The two fluorescing photons are emitted virtuallysimultaneously, i.e., within a time period of about 10 femto-seconds,and, depending on the type of nonlinear crystal and the excitationgeometry, in the same or in different spatial directions. Thepolarization of the fluorescing photons is thereby established. Thephysical properties of the two photons of the parametric fluorescenceare linked to one another by a number of secondary conditions. In thecase of the transposed photons, it may be a question, quantummechanically, of a single state in which two photons reside inseparably,measurements at one of the photons allowing precise information to beobtained regarding the physical properties of the corresponding otherphoton.

The reference German Patent Application No. DE 198 23 849.5 purportedlydescribes a method and a device for optionally generating individualphotons or photon pairs in an optical channel, by way of which a photonpair, in a quantum mechanically transposed state, is able to beselectively spatially separated, or propagated colinearly, as a pair. Inpurported accordance with the reference German Patent Application No. DE198 23 849.5, from a photon pair source, photon pairs are generated in aquantum mechanically transposed state, and one photon of the pair iscoupled into one partial path of rays of the device, respectively, thetwo partial paths of rays being reunited at a beam splitter and beingdirected into two common output channels. Positioned in the firstpartial path of rays is an interferometer, whose interferometer armshave optical path lengths δl_(F) and δl_(S). Positioned in the secondpartial path of rays is an optical delay path of optical length δl.Using means for varying optical path lengths δl_(F), δl_(S) and/or δl,these path lengths are adjustable such that photon pairs are generatedwhich, as the result of interference, propagate co-linearly orseparately in the output channels of the beam splitter. The adjustmentis made, for example, via the measurement of the coincidences or spatialcoincidences between the output channels.

The separation of the pairs in the context of the system discussed inthe reference German Patent Application No. DE 198 23 849.5 is believedto be based on the quantum state of the one photon being split into twopreferably separate probability distributions in the state space whichhave different, namely orthogonal polarization, and are spatiallyseparate from one another. This probability distribution is achieved inthat the photon propagates through a polarizing interferometer, which,for example, is a double-refractive crystal or an interferometer, whosedesign includes polarizing beam splitters aligned at less than 45° tothe polarization of the photon. Due to the different optical pathlengths in the interferometer arms, a photon is generated. Theprobability that it resides in the local space has two maxima, whichpropagate at the speed of light along the same light path and includestates having orthogonal polarization. Such a photon, propagating in thez-direction, is shown, for example, schematically in FIG. 1. At Z1, thewave packet is horizontally linearly (y-direction) and, at Z2,vertically linearly polarized.

In this quantum state, the probabilities of finding the photon at Z1 andZ2 are differently polarized may be a drawback. Since it is always onlyindistinguishable photons which interfere with one another, the tworesidence probability regions around Z1 and Z2 should have the samepolarization, to be optimally further processed and to be brought intointerference with the photon in the second partial path of rays. Thepolarizations of the two regions Z1, Z2 can be compensated or made morealike in that the photon in the first partial path of rays propagatesthrough a linear polarizer, which is situated at less than 45° withrespect to the x- and y-axis. Here, half of the correlated photon pairsmay be lost in this manner.

SUMMARY OF THE INVENTION

Exemplary embodiments and/or exemplary methods of the present inventionmay be directed to allowing selective changing of the polarization ofone photon of a photon pair, and further, the polarization distributionof such a photon.

Exemplary embodiments and/or exemplary methods of the present inventionmay be directed to improving the efficiency of the method purportedlydescribed in the reference German Patent Application No. DE 198 23 849for optionally generating single photons or photon pairs in an opticalchannel.

Exemplary embodiments and/or exemplary methods of the present inventionmay be directed to changing the polarization of at least one of thephotons emitted from a photon pair source into various partial ray pathsusing an electro-optical modulator (EOM), which is positioned in theparticular partial ray path being traversed by the photon to beinfluenced and which, in the activated state, is able to alter thepolarization of a photon, where the modulator (EOM) is activated as afunction of time such that the probability that the photon is found inthe region of the electro-optical modulator (EOM) in the activated stateis at a maximum, and the modulator (EOM) must be deactivated followingpassage through the maximum. Further or in addition to, the photon-pairsource may be an optically non-linear crystal that is pumped using apulsed laser, and the instant when the modulator (EOM) is activated(activation instant), may be determined from the pulse-repetition rateand from the optical path length from the crystal to the electro-opticalmodulator (EOM), and/or the activation instant for influencing the onephoton may be determined from the registration instant of the otherphoton, the other photon being registered without being destroyed.

Exemplary embodiments and/or exemplary methods of the present inventionmay be further directed to optionally generating individual photons orphoton pairs in an optical channel using a photon-pair source, thephotons of one photon pair being coupled into one partial path of raysof the device, and the two partial ray paths being united at a beamsplitter and directed into two shared output channels of aninterferometer positioned in the first partial ray path, as well asmeans for changing the optical path lengths of the interferometer armsand/or of the second partial path of rays, in the first partial ray pathdownstream from the interferometer, an electro-optical modulator (EOM)being positioned, which, in the activated state, is able to alter thepolarization of a photon, where the modulator (EOM) is activated as afunction of time such that the probability that the photon is found inthe region of the electro-optical modulator (EOM) in the activated stateis at a maximum, and the modulator (EOM) must be deactivated followingpassage through the maximum. Further or in addition to, the photon-pairsource may be an optically non-linear crystal that is pumped using apulsed laser, and the instant when the modulator is activated(activation instant), being determined from the pulse-repetition rateand from the optical path length from the crystal to the electro-opticalmodulator, and/or the activation instant for influencing the one photonmay be determined from the registration instant of the other photon, theother photon being registered without being destroyed, and/or theactivation instant of the modulator (EOM) is determined from the opticalpath length of one or both interferometer arms.

In this context, the interferometer may be a polarizing interferometer,which is positioned at less that 45° with respect to the polarizationdirection of the photon radiated into the first partial ray path.

Thus, in accordance with the present invention, the modulator may beactivated as a function of time such that it is able to influenceprecisely that part of the photon's wave function whose polarization isto be changed. In the case of a photon having a nearly Gaussian-shapedprobability distribution in the local space and constant polarization,the modulator may be activated already before the photon's arrival atthe modulator, i.e., before the maximum of the residence probability orprobability of finding the photon at the modulator is reached. Themodulator is deactivated after the local residence probability hasreturned to zero, i.e., the photon has left the modulator. If the nextphoton is to be influenced, the modulator may also remain in anactivated state. In the case of a photon having a split probabilitydistribution, such as in FIG. 1, the modulator is activated such that itonly influences the region around one of the maxima of the probabilitydistribution.

If the first maximum, e.g., in FIG. 1 that around Z1, is to bemanipulated, the modulator is, therefore, activated in a timely fashionbefore arrival of this partial wave packet, and is again deactivated,before arrival of the further partial wave packet, e.g., in FIG. 1 withthe maximum around Z2. In this case, the duration of activation or theinstant of deactivation is to be adapted to the time interval of the twopartial wave packets and to be precisely observed, in order not tochange the polarization of the second partial wave packet. Depending onthe optical properties of the electro-optical modulator, in particularthe activation and decay time, it may be practical to influence thesecond part of the wave packet. In this case, the activation instantmust be precisely observed, the deactivation instant being lesscritical. For that reason, a modulator having a greater decay time mayalso be selected, it being necessary, however, for the modulator to befully deactivated again and to be able activated upon arrival of thenext photon.

When a photon-pair source working in pulsed operation is used, which ispreferably an optically non-linear crystal that is pumped using a pulsedlaser, the instant when the modulator is activated (activation instant),is preferably determined from the pulse-repetition rate and from theoptical path length from the crystal to the electro-optical modulator.By performing a comparison measurement, one is able to determine theinstants when the photon pairs are generated from the repetition rateand the distance of the detector from the photon-pair source. From theoptical path length from the photon pair source to the modulator, it ispossible to determine at which instant within any one cycle, the photonarrives at the modulator and the modulator is to be activated.

When individual photons or photon pairs are optionally generated, theactivation and/or deactivation instant of the modulator is/arepreferably determined from the optical path length of one or bothinterferometer arms. Based on knowledge of the remaining path lengthsfrom the photon-pair source to the modulator, the activation instantwhen the earlier partial wave packet is to be influenced is derived fromthe photon's propagation time through the shorter interferometer arm.The activation operation is such that, upon arrival of the earlierpartial wave packet, the modulator is already active, and, upon arrivalof the later partial wave packet, it is already deactivated. If thelater partial wave packet is to be influenced, then the modulator isswitched on such that it is activated only upon arrival of the laterpartial wave packet. The accuracy required for activation in this caseis derived from the transit-time difference between the twointerferometer arms.

Alternatively or additionally thereto, the activation instant forinfluencing the one photon is determined from the registration instantof the other photon and from the particular optical path lengths. Sincethe intention is to continue to use both photons, the other photon isregistered without destroying it. In principle, the photon may bedetected in a non-destructive manner, in that it propagates through anon-linear medium, such as individual, highly excited atoms (Rydbergatoms). As the photon passes through, the medium changes its refractiveindex. This change in the refractive index is registeredinterferometrically by a test laser beam (so-called “quantumnondemolition” measurement).

To ensure that it is only the photons of a particular photon pair thatare influenced, it is proposed that the period of activation of themodulator be shorter by at least half than the period duration of thepulsed photon-pair source.

Most applications require a modulator which is able to rotate thepolarization of the photon or that of the partial-wave packet by 90°.For example, the electro-optical modulator is a λ/2 delay element, whichis quickly rotated or switched on or off to change the polarization ofthe photon. As a modulator, a Pockel or Kerr cell is used on the basisof non-linear optical crystals, such as KDP, LiNbO₃, or on the basis ofsemiconductor materials such as GaAs. At the present time, thesemodulators have the capability of being switched with time constants inthe nanosecond range; future development provides for further reductionsin the typical time constants. A switching time of 1 ns signifies thatthe two residence probabilities of the photon must be set apart by aboutone meter to enable them to be separated.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a photon having two residence probability regions oforthogonal, linear polarization.

FIG. 2 shows a set-up for implementing the method(s) according to thepresent invention.

FIG. 3 shows the residence probability and polarization of a photon atvarious locations of the set-up of FIG. 2.

FIG. 4 shows a set-up for optionally generating individual photons orphoton pairs using a polarizing beam splitter.

DETAILED DESCRIPTION

FIG. 1 schematically illustrates the spatial residence probability andpolarization of a photon propagating along the z-axis, based on theexample of two residence probability regions. In the region around Z1,it is linearly polarized in the y-direction; in the region around Z2, itis linearly polarized in the x-direction. Such a wave function orresidence probability is achieved using a polarizing interferometer,which is oriented at less than 45° to the photon's startingpolarization, so that both interferometer arms are passed through withequal probability. Here, the residence probabilities around Z1 and Z2are separated by a region in which the residence probability is zero.The distance Z1-Z2 may be given by the optical path length difference inthe interferometer arms. The greater the distance Z1-Z2 is, the moreeasily the two regions may be able to be separately influenced.

FIG. 2 illustrates a set-up for implementing the method for selectivelychanging the polarization of a photon in accordance with embodimentsand/or methods of the present invention. Using a highly coherentintensive laser hv, in non-linear crystal 1, parametric fluorescenceproduces photon pairs which propagate through partial ray paths A1 andA2. The pump photon decays into two photons of about half energy.Depending on the type of decay, photons may be formed which areidentically (type I) or orthogonally (type II) polarized.

Partial ray paths A1 and A2 are deflected by two mirrors SP3 and SP4 ata beam splitter ST1 and directed by this beam splitter into two sharedoutput channels D1 and D2.

An interferometer may be positioned in first partial ray path A1. Theinterferometer is a polarizing Mach-Zehnder interferometer which ispositioned at less than 45° to the polarization direction of the firstphoton. It is made up of two polarizing beam splitters PST1 and PST2 andtwo mirrors SP1 and SP2, of which SP1 is electrically adjustable by apiezoceramic element 4. Beam splitter PST1 guides partial ray path A1into the two interferometer arms 2 and 3; PST2 reunites them. Anadditional delay path in interferometer arm 3 permits delays of variablelengths, up to the meter range. Subsequent to beam splitter PST2 in theoutput of the interferometer, the probability residence of the photon,as shown in FIG. 1, is split into two regions Z1, Z2, which are variablypolarized.

In accordance with the present invention, an electro-optical modulatorEOM is positioned in first partial ray path A1 to selectively change thepolarization of the photon. This modulator splits the partial ray pathat the interferometer, into two regions B1 and C1. Modulator EOM may beused in accordance with the present invention to adjust the polarizationof the one half of the double-peak photon wave packet to thepolarization of the other half. The EOM may be electrically driven insuch a way that it only influences one of the two partial wave packets.It must be fast enough to enable the switching to be performed in theintermediate region between Z1 and Z2 (compare FIG. 1). As a modulator,a rapidly switchable λ/2 delay plate may be used, which is eitherrapidly rotatable or switchable on and off for purposes of activation ordeactivation.

By adapting the optical path lengths of the interferometer arms 2, 3 andof second partial ray path A2, as described in the reference GermanPatent Application No. DE 198 29 849.5, photon pairs or individualphotons may be optionally generated. This process can be twice asefficient when the polarization state of the first photon is changed inaccordance with the present invention.

FIG. 3 illustrates the residence probability and the polarization of aphoton at various locations of the set-up of FIG. 2. Immediately uponarrival in first partial ray path A1, the photon is linearly polarizedunder 45°. After propagating through the polarizing interferometer, thephoton in region B1 exhibits a residence probability, having orthogonalpolarization, concentrated in two regions around Z1 and Z2, asillustrated in FIG. 2 and described. Using electro-optical modulatorEOM, the polarization of the partial wave packet may be changed by Z1and is adapted to the polarization of the other partial wave packet,region Cl. This thus manipulated first photon is brought intointerference with the second photon of the photon pair by beam splitterST1.

FIG. 4 depicts another system for optionally generating individualphotons or photon pairs employing a polarizing beam splitter PST3 andpolarization manipulation in accordance with the present invention. Asin the set-up from FIG. 2, using a highly coherent, intensive laser hv,in non-linear crystal 1, parametric fluorescence produces photon pairswhich propagate through partial ray paths A1 and A2. The partial raypaths are reunited via two mirrors at a polarizing beam splitter PST3and directed into two shared output channels D1 and D2. In a describedmanner, to change over the polarization of the particular photon, anelectro-optical modulator EOM1, EOM2 is positioned in both partial raypaths A1, A2.

If the photons of the photon pair meet beam splitter PST3 with the same,e.g., linear, vertical polarization, then both are reflected. If theymeet beam splitter PST3 with polarization that is orthogonal thereto,e.g., linear, horizontal, then both are transmitted. In both cases, onereceives individual photons in outputs D1 and D2. Variably orthogonallypolarized photons arrive as a pair in one of outputs D1 or D2.

The polarization of one of the photons may be selectively switched overby modulators EOM1, EOM2, making it possible to determine in whichoutput it arrives. In this manner, photon pairs may also be selectivelyproduced. As described, the modulators' switching times are determined,for example, from the repetition rate and the path lengths. Since theprobability distribution of the photons is not split, activation of themodulator may begin prior to arrival of the photon; it is not necessaryfor the modulator to be activated or deactivated as rapidly as in thecase of polarization change within the same photon-wave function. Itsuffices when the modulator is deactivated up until the next cycle, andis able to be activated again.

The present invention may be used, among other things, for example, inthe field of quantum computers and quantum cryptography to furtherenhance efficiency.

1. A method for changing the polarization of at least one of the photonsemitted from a photon pair source into various partial ray paths usingan electro-optical modulator, which is positioned in a first ray pathbeing traversed by the photon to be influenced and which, in theactivated state, is able to alter the polarization of a photon, whereinthe modulator is activated as a function of time such that theprobability that the photon is found in the region of theelectro-optical modulator in the activated state is at a maximum, andthe modulator must be deactivated following passage through the maximum,the photon-pair source being an optically non-linear crystal that ispumped using a pulsed laser, and the instant when the modulator isactivated (activation instant) being determined from thepulse-repetition rate and from the optical path length from the crystalto the electro-optical modulator; and/or the activation instant forinfluencing the one photon being determined from the registrationinstant of the other photon, the other photon being registered withoutbeing destroyed.
 2. A method for optionally generating individualphotons or photon pairs in an optical channel using a photon-pairsource, the photons of one photon pair being coupled into one partialpath of rays of the device, and the two partial ray paths being unitedat a beam splitter and directed into two shared output channels of aninterferometer positioned in the first partial ray path, as well asmeans for changing the optical path lengths of the interferometer armsand/or of the second partial path of rays, in the first partial ray pathdownstream from the interferometer, an electro-optical modulator beingpositioned, which, in the activated state, is able to alter thepolarization of a photon, wherein the modulator is activated as afunction of time such that the probability that the photon is found inthe region of the electro-optical modulator in the activated state is ata maximum, and the modulator must be deactivated following passagethrough the maximum, the photon-pair source being an opticallynon-linear crystal that is pumped using a pulsed laser, and the instantwhen the modulator is activated (activation instant), being determinedfrom the pulse-repetition rate and from the optical path length from thecrystal to the electro-optical modulator; and/or the activation instantfor influencing the one photon being determined from the registrationinstant of the other photon, the other photon being registered withoutbeing destroyed; and/or the activation instant of the modulator beingdetermined from the optical path length of one or both interferometerarms.
 3. The method of claim 2, wherein the interferometer is apolarizing interferometer, which is positioned at less that 45° withrespect to the polarization direction of the photon radiated into thefirst partial ray path.
 4. The method of claim 1, wherein the modulatoris able to rotate the polarization of the photon by 90°.
 5. The methodof claim 2, wherein the modulator is able to rotate the polarization ofthe photon by 90°.
 6. The method of claim 1, wherein the electro-opticalmodulator is a λ/2 delay element, which is quickly rotated or switchedon or off to change the polarization of the photon.
 7. The method ofclaim 2, wherein the electro-optical modulator is a λ/2 delay element,which is quickly rotated or switched on or off to change thepolarization of the photon.
 8. The method of claim 1, wherein the periodof activation of the modulator is shorter by at least half than theperiod duration of the pulsed photon-pair source.
 9. The method of claim2, wherein the period of activation of the modulator is shorter by atleast half than the period duration of the pulsed photon-pair source.